Ch 15 - Chi-Squared _Categorical Data_

As we can see the null hypothesis is stating that the

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Unformatted text preview: ls. Question: Is Ice Cream Preference the same for boys and girls? Data: 1 random sample of 75 preschool boys, 1 random sample of 75 preschool girls; the two random samples are independent. The table below summarizes the data in terms of the observed counts. Observed Counts: Ice Cream Preference Boys Girls Vanilla (V) 25 26 Chocolate (C) 30 23 Strawberry (S) 20 26 75 75 Note: The column totals here were known in advance, even before the ice cream preferences were measured. This is a key idea for how to distinguish between the test of homogeneity and the test of independence. The null hypothesis: H0: The distribution of ice cream preference is the same for the two populations, boys and girls. A more mathematical way to write this null hypothesis is: H0: P X i | population j P X i for all i, j where X is the categorical variable, in this case, ice cream preference. As we can see, the null hypothesis is stating that the distribution of ice cream preference does not depend on (is independent of) the population we select from since the two distributions are the same. The null hypothesis looks like: P A | B P A , which is one definition of independent events, from our previous discussion of independence. This is why the test of homogeneity (comparing several populations) is really the same as the test of independence. The assumptions are different however. For our homogeneity (comparing several populations) test, we assume we have independent random samples, one from each population, and we measure 1 discrete (categorical) response. For the independence test (discussed later) we will assume we have just 1 random sample from 1 population, but we measure 2 discrete (categorical) responses. 211 Getting back to our ICE CREAM ... The two‐way table provides the OBSERVED counts. Our next step is to compute the EXPECTED counts, under the assumption that H0 is true. How to find the expected counts? Let's look at those who preferred Strawberry first. Strawberry: Since there were 46 children who prefe...
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